2010 AIME II Problem 2

A point P is chosen at random in the interior of a unit square S. Let d(P) denote the distance from P to the
closest side of S. The probability that \frac{1}{5} \leq d(P) \leq \frac{1}{3} is equal to \frac{m}{n}, where m
and n are relatively prime positive integers. Find m+n.